We analyze the computational complexity of the problem of optimally managing a storage device connected to a source of renewable energy, the power grid, and a household (or some other form of energy demand) in the presence of uncertainty. We provide a mathematical formulation for the problem as a Markov decision process following other models appearing in the literature, and study the complexit...

In the present article, we propose the $(p,q)$ variant of genuine Baskakov Durrmeyer operators. We obtain moments and establish some direct results, which include weighted approximation and results in terms of modulus of continuity of second order.

In this paper we study the Multiple Strip Packing (MSP) problem, a generalization of the well-known Strip Packing problem. For a given set of rectangles, r1, . . . , rn, with heights and widths ≤ 1, the goal is to find a non-overlapping orthogonal packing without rotations into k ∈ N strips [0, 1]× [0,∞), minimizing the maximum of the heights. We present an approximation algorithm with absolute...

This paper presents the first approximation algorithms and the first inapproximability results for minmax path cover problems, where a capacity constraint restricts the number of customers that can be serviced by every trip of the paths in the cover. Depending on different applications, every path in the cover may either be restricted to contain only one trip, or be allowed to contain multiple ...

The three art gallery problems Vertex Guard, Edge Guard and Point Guard are known to be NP -hard [8]. Approximation algorithms for Vertex Guard and Edge Guard with a logarithmic ratio were proposed in [7]. We prove that for each of these problems, there exists a constant > 0, such that no polynomial time algorithm can guarantee an approximation ratio of 1 + unless P = NP . We obtain our results...

In generalized Lebesgue spaces $L^{p(.)}$ with variable exponent $p(.)$ defined on the real axis, we obtain several inequalities of approximation by integral functions finite degree. Approximation properties Bernstein singular integrals in these are obtained. Estimates simultaneous degree proved.

In this work we prove optimal W s,p-approximation estimates (with p P r1,`8s) for elliptic projectors on local polynomial spaces. The proof hinges on the classical Dupont– Scott approximation theory together with two novel abstract lemmas: An approximation result for bounded projectors, and an Lp-boundedness result for L2-orthogonal projectors on polynomial subspaces. The W s,p-approximation re...